How to model a ridged cone (using modifiers)?
Here is a way to do it:


Create a plane, go in Edit mode, rotate on the X axis and scale it, move it a bit away from its origin on the Y axis.
Cut it in half with a vertical edge loop, give it a Mirror modifier, enable the Clipping option.
Create an empty on the same position as the plane origin.
Select the plane, give it an Array modifier, deactivate Relative Offset and activate  Object Offset, choose the empty as the Object. Choose a Count of, for example, 18. Activate the Merge and First Last options.
Rotate the empty 20° on the Z axis.
Select the plane, go in Edit mode and edit the plane mesh, move the vertices, add some vertical edge loops.
Give your plane a Subsurf modifier, add some horizontal edge loops.
When you'll be glad with the result, keep a copy, then apply all the modifiers except the Subsurf, remove the doubles, close the top with some altM > Merge.